Method for identifying individual radiation sources in a finite sample scenario under digital pre-distortion

Abstract

The application relates to a method for identifying a radiation source individual in a limited sample scene under digital pre-distortion, and belongs to the field of radiation source individual identification. The application aims to solve the problem of low radiation source individual identification accuracy caused by the application of DPD technology in actual deployment and insufficient data in online SEI deployment. The method for identifying a radiation source individual in a limited sample scene under digital pre-distortion comprises the following steps: pre-processing collected signals to obtain HHT, ITD-Hilbert, CWT, CWD and GT; pre-processing HHT graphs, ITD-Hilbert graphs, CWT graphs, CWD graphs and GT graphs respectively to construct a data set; constructing an FS-SEI network model; the FS-SEI network model comprises a CNN network model and a relationship network model; the CNN network model comprises a feature extractor and a classifier in sequence; training the CNN FS-SEI network model to obtain a trained FS-SEI network model; inputting a test set into the trained FS-SEI network model, and outputting the class of the test set by the trained FS-SEI network model.

Description

TECHNICAL FIELD

[0001] The application relates to a radiation source individual identification method and belongs to the field of radiation source individual identification. BACKGROUND

[0002] With the proliferation of wireless devices, securing the physical layer with strong security remains a major challenge. The primary purpose of SEI is to identify the transmitter by analyzing the unique characteristics of unintentional modulation of pulses (UMOP) in the signal. Compared with software-based security credentials, UMOP remains stable in nature and is particularly resistant to changes, so SEI has become an essential element in various wireless communication environments. Before the advent of deep learning (DL), traditional SEI methods mainly relied on statistical methods to design features, including high-order spectrum, cumulants, nonlinear dynamic features, and various time-frequency (TF) features derived from transforms such as short-time Fourier transform. However, these traditional methods are significantly limited, including subpar performance, limited adaptability to different environments, and inability to cope with escalating complexity and numerous transmitters. In recent years, deep learning has become a promising data analysis tool and has gained widespread attention in wireless communication technology, particularly in the field of SEI. Deep learning-based SEI methods utilize neural networks such as convolutional neural networks (CNN), recurrent neural networks (RNN), transformer models, and generative adversarial networks (GAN) to achieve unified feature extraction and classification. These deep learning-based SEI methods are divided into three main parts according to sample representation: time-domain signals, spectrograms, and constellation diagrams. Deep learning-based SEI techniques utilize a large repository of historical samples to extract more flexible and effective UMOP features, offering superiority over methods that rely on artificially designed features. However, these methods face limitations in the availability of training signal samples for new classes and the opportunity for retraining during online deployment.

[0003] Amplifier nonlinear distortion is a major factor in SEI. However, in communication and radar systems, this distortion not only narrows the linear range but also reduces overall efficiency. As these systems demand increasingly wider bandwidths, linearization amplifiers and methods to improve efficiency, such as negative feedback, envelope tracking, and digital predistortion (DPD), have also emerged. DPD technology stands out among various linearization techniques due to its flexible digital algorithms, compensation capabilities, adaptability, and lower power consumption. Compared with other linearization methods, it can achieve a simpler circuit configuration to achieve a wider bandwidth, making it increasingly favored for PA linearization compensation. Currently, various DPD methods have been proposed, including piecewise linear, discrete Newton, least mean square (LMS) algorithm, rotation and scaling (RASCAL), and recursive least squares (RLS) algorithm. However, it is worth noting that while DPD technology alleviates amplifier nonlinearities in the transmitting extreme, it may inadvertently weaken SEI performance. SUMMARY

[0004] The application aims to solve the problem of low accuracy of individual identification of radiation sources caused by the application of DPD technology in actual deployment and insufficient data in online SEI deployment, and proposes a method for individual identification of radiation sources in a limited sample scenario under digital pre-distortion.

[0005] The method for individual identification of radiation sources in a limited sample scenario under digital pre-distortion specifically comprises the following steps:

[0006] Step one, pre-process the collected signals to obtain HHT, ITD-Hilbert, CWT, CWD and GT graphs;

[0007] The HHT is Hilbert-Huang transform;

[0008] The ITD-Hilbert is Hilbert transform;

[0009] The CWT is continuous wavelet transform;

[0010] The CWD is Choi-Williams distribution;

[0011] The GT is Gabor transform;

[0012] Step two, pre-process the HHT, ITD-Hilbert, CWT, CWD and GT graphs respectively, and construct a data set;

[0013] Step three, construct an FS-SEI network model;

[0014] The FS-SEI network model comprises a CNN network model and a relationship network model;

[0015] The CNN network model comprises a feature extractor and a classifier in sequence;

[0016] Step four, train the FS-SEI network model to obtain a trained FS-SEI network model;

[0017] Step five, input the test set into the trained FS-SEI network model, and the trained FS-SEI network model outputs the class of the test set.

[0018] The application has the following advantages:

[0019] The application is a few-sample radiation source individual identification (FS-SEI) model, which integrates convolutional neural network (CNN) embedding and metric learning, and is suitable for scenarios with limited sample availability.

[0020] The present invention characterizes signals through the Hilbert-Huang Transform (HHT), ITD-post-Hilbert Transform (ITD-Hilbert), Continuous Wavelet Transform (CWT) and Choi-Williams Distribution (CWD), Gabor Transform (GT). These methods help to represent various forms of emitter signals as time-frequency images, thus revealing different features of the signals.

[0021] The present invention proposes a FS-SEI model under DPD. The model integrates a CNN for deep feature vector extraction and a relational network (RN) aiming to autonomously learn a non-linear distance metric. Our research results show that, although DPD techniques tend to mask the unique features of emitters, the FS-SEI model successfully copes with this challenge, showing a significant performance improvement over traditional CNNs and other methods in the SEI task. This enhancement is particularly significant in environments with low signal-to-noise ratio and limited sample availability. As DPD techniques continue to evolve and become more integrated into modern communication systems, it is interesting to improve SEI methods under these conditions. BRIEF DESCRIPTION OF DRAWINGS

[0022] Figure 1 FS-SEI model framework under DPD;

[0023] Figure 2 Feature extraction network diagram;

[0024] Figure 3 Relational network architecture diagram;

[0025] Figure 4 SEI results under different signal representation methods, a based on ResNet50 model, b based on FS-SEI model;

[0026] Figure 5 SEI results under different dimensions of CNN feature vectors, a SEI results, b complexity analysis;

[0027] Figure 6 SEI results under different dimensions of CNN feature vectors, a K = 1, b K = 5, c K = 10, d K = 20, e K = 50, f K = 100;

[0028] Figure 7 FS-SEI results under different signal-to-noise ratios with K = 10, a SNR = -5 dB, accuracy = 77.07%; b SNR = 10 dB, accuracy = 97.21%. DETAILED DESCRIPTION

[0029] Specific embodiment one: the specific process of the method for identifying the individual of the radiation source in the limited sample scene under the digital pre-distortion is as follows:

[0030] Step one: the collected signals are pre-processed to obtain HHT graph, ITD-Hilbert graph, CWT graph, CWD graph and GT graph (time-frequency graph);

[0031] The HHT is Hilbert-Huang transform;

[0032] The ITD-Hilbert is Hilbert transform;

[0033] The CWT is continuous wavelet transform;

[0034] The CWD is Choi-Williams distribution;

[0035] The GT is Gabor transform;

[0036] Step two: the HHT graph, ITD-Hilbert graph, CWT graph, CWD graph and GT graph are pre-processed respectively to construct a data set;

[0037] Step three: an FS-SEI (radiation source individual identification under few samples) network model is constructed;

[0038] The FS-SEI network model includes a CNN network model and a relationship network model;

[0039] The CNN network model includes a feature extractor and a classifier in sequence;

[0040] A simple and effective CNN architecture is designed for the FS-SEI, including a double-component system of the feature extractor and the classifier, as shown in Figure 2 .

[0041] The CNN feature vector is taken as the input to realize CNN feature embedding, the CNN feature vector extracted through the metric learning is implemented clustering, and the SEI performance of the traditional CNN is enhanced;

[0042] Step four: the CNN FS-SEI network model is trained to obtain the trained FS-SEI network model;

[0043] Step five: the test set is input into the trained FS-SEI network model, and the trained FS-SEI network model outputs the category of the test set.

[0044] Specific embodiment two: the difference between the specific embodiment two and the specific embodiment one is that the collected signals are pre-processed to obtain HHT, ITD-Hilbert, CWT, CWD and GT (time-frequency graph) in the step one, and the specific process is as follows:

[0045] Step one-one, different types of transmitters (power amplifier chip model, aging length, different types of transmitters) collect signal samples;

[0046] Wavelet denoising is performed on the collected signal samples to obtain denoised signal samples;

[0047] Pulse extraction is performed on the denoised signal samples, and every 10 pulses are taken as one signal sample to obtain 500 signal samples;

[0048] Each of the 10 pulses in each signal sample is extracted to obtain a signal sample containing only a single pulse;

[0049] A total of 5000 signal samples containing only a single pulse are obtained;

[0050] Step two, Hilbert-Huang transform is performed on the signal containing only a single pulse obtained in step one to obtain an HHT time-frequency diagram;

[0051] Step three, first perform intrinsic time-scale decomposition on the signal containing only a single pulse obtained in step one to obtain a rotating component, and then calculate the Hilbert spectrum of the rotating component to obtain an ITD-Hilbert time-frequency diagram;

[0052] Step four, take Morlet wavelet as mother wavelet ψ(·), and perform scaling and translation on the mother wavelet ψ(·) to generate A wavelet functions;

[0053] Calculate the convolution of the signal x(t) containing only a single pulse obtained in step one and each wavelet function ψ(t) to produce a signal representation across different time and frequency scales, and obtain a CWT time-frequency diagram; the expression is:

[0054]

[0055] Where a represents the scale parameter of the wavelet function, b represents the translation parameter, ψ * (·) represents the complex conjugate of the mother wavelet, and t represents time;

[0056] This equation facilitates multi-scale and multi-position signal analysis by adjusting the scale a and translation b values;

[0057] Step five, calculate the Choi-Williams distribution of the pulse signal to obtain a CWD time-frequency diagram; the expression is:

[0058] CWD can effectively improve the recognizability of transmitter characteristics through its unique time-frequency analysis characteristics. It provides a clearer time-frequency representation by reducing the interference of cross terms, which is particularly important for distinguishing signals from different transmitters.

[0059]

[0060] where x(t) represents the signal containing only a single pulse obtained in step one, x * (t) represents the complex conjugate of x(t), σ represents a parameter for controlling the gentleness of the distribution, f represents frequency, t represents time, τ represents a time delay variable, which is used to represent the shift of the wavelet function on the time axis, by changing τ, the wavelet function can be compared and analyzed with the signal at different time positions, j represents the imaginary unit, j 2 = -1.

[0061] e -j2πfτ is a complex exponential function, which is used to realize the conversion of the signal in the frequency domain. This term is responsible for converting the delay τ information in the time domain to f in the frequency domain.

[0062] is a Gaussian window function, which is used to weight the signal in the τ domain, where σ controls the width of the window. The influence of the cross term is reduced, thereby enhancing the clarity of the time-frequency depiction.

[0063] Step one six, performing Gabor transform on the signal containing only a single pulse obtained in step one one, to obtain a GT time-frequency map.

[0064] Step one seven, storing the HHT time-frequency map, the ITD-Hilbert time-frequency map, the obtained CWT time-frequency map, the CWD time-frequency map, and the GT time-frequency map with a size of 700x525.

[0065] The other steps and parameters are the same as in the first embodiment.

[0066] Specific embodiment three: the difference between this embodiment and the first or second embodiment is that the HHT time-frequency map, the ITD-Hilbert time-frequency map, the CWT time-frequency map, the CWD time-frequency map, and the GT time-frequency map are respectively preprocessed in step two to construct a data set; the specific process is as follows:

[0067] Step two one, randomly dividing the signal sample data set containing only a single pulse obtained in step one one into a training set and a test set according to a ratio of 7:3; the training set is further divided into two parts, K samples are used for training, and the remaining samples are used for verification.

[0068] Step two, the HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram and GT time-frequency diagram obtained in step one are subjected to normalization operation respectively to obtain normalized HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram and GT time-frequency diagram, and the normalized HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram and GT time-frequency diagram are respectively cropped into HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram and GT time-frequency diagram with a size of 100*100;

[0069] Step two, the HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram and GT time-frequency diagram obtained in step one are subjected to normalization operation respectively to obtain normalized HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram and GT time-frequency diagram, and the normalized HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram and GT time-frequency diagram are respectively cropped into HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram and GT time-frequency diagram with a size of 100*100;

[0070] One folder represents the signal secondary representation of different forms of time-frequency diagrams corresponding to the same type of transmitter.

[0071] The other steps and parameters are the same as those in specific embodiment one or two.

[0072] Specific embodiment four: the difference between this embodiment and one of specific embodiments one to three is that the FS-SEI network model is constructed in step three.

[0073] The FS-SEI network model includes a CNN network model and a relationship network model.

[0074] The CNN network model sequentially includes a feature extractor and a classifier.

[0075] The specific process is as follows:

[0076] Step three, a CNN network model is constructed, which sequentially includes a feature extractor and a classifier.

[0077] The feature extractor sequentially includes a first convolutional block, a max-pooling layer, a second convolutional block, a max-pooling layer, a third convolutional block, a max-pooling layer, a flattening layer Faltten, a fully connected layer FC, a batch normalization BN and a linear rectifier function ReLU.

[0078] The classifier sequentially includes a fully connected layer FC, a batch normalization BN, a linear rectifier function ReLU, a fully connected layer FC, a batch normalization BN, a linear rectifier function ReLU and a Softmax layer.

[0079] Each of the first convolutional block, the second convolutional block and the third convolutional block comprises, in sequence, a convolutional layer (Conv), a batch normalization (BN), and a rectified linear unit (ReLU);

[0080] The task of the feature extractor is to further refine the graph into a 1024-dimensional feature vector, which is then introduced into a CNN classifier and a relationship network.

[0081] Step three two, constructing a relationship network model;

[0082] The relationship network model comprises, in sequence, a concatenation layer, a flattening layer (Faltten), a fully connected layer (FC), a batch normalization (BN), a rectified linear unit (ReLU), a fully connected layer (FC), a batch normalization (BN), a rectified linear unit (ReLU), a fully connected layer (FC), a batch normalization (BN), a rectified linear unit (ReLU), a fully connected layer (FC), and a sigmoid activation function.

[0083] The other steps and parameters are the same as those in one of the first to third embodiments.

[0084] Embodiment five: The embodiment is different from one of the first to fourth embodiments in that the FS-SEI network model is trained in step four to obtain a trained FS-SEI network model; the specific process is as follows:

[0085] Step four one, inputting the signal secondary representation into a CNN network model, and the CNN network model outputs a transmitter type result; the specific process is as follows:

[0086] Inputting the cropped HHT time-frequency graph, the ITD-Hilbert time-frequency graph, the CWT time-frequency graph, the CWD time-frequency graph and the GT time-frequency graph corresponding to the signal secondary representation into a feature extractor, and the feature extractor outputs a 1024-dimensional feature vector;

[0087] Inputting the 1024-dimensional feature vector into a classifier, and the classifier outputs a transmitter type result;

[0088] Step four two, inputting the 1024-dimensional feature vector into a relationship network model, and the relationship network model outputs a relationship score;

[0089] Step four three, training the CNN network model until convergence, and obtaining a trained CNN network model; the specific process is as follows:

[0090] The loss function is J(θ), and in order to minimize the loss function J(θ), a stochastic gradient descent (SGD) algorithm is used to optimize the CNN network model;

[0091]

[0092] wherein J(θ) is the loss function;

[0093] Represents the secondary representation of the signal, output represents the probability that the signal belongs to each emitter category; C, H, W, and N represent the number of channels, height, width, and category, respectively. represents the set of real numbers;

[0094] M represents the total number of training samples; i and n represent the indexes of training samples and emitter categories, respectively; y i Represents the category label; θ represents the parameters of the CNN network model;

[0095] When the true label of the i-th training sample is consistent with n, the p value is 1; otherwise, the p value is 0;

[0096] P θ Represents the output of the softmax layer in the classifier;

[0097] The feature extractor output in the CNN network model is experimentally selected to be 1024-dimensional.

[0098] Step 4: Train the relational network model until convergence to obtain a trained CNN network model. The specific process is as follows:

[0099] Step 441: Define the support set and queryset

[0100] Among them, f θ (x i ) represents the feature extractor f θ The CNN feature vector extracted from the examples in the support set S, f θ (x j ) represents the CNN feature vector extracted by the feature extractor from the examples of the query set Q;

[0101] Where M represents the number of support set samples, S includes all training set samples, and when the support set S contains N emitter categories and each category has K samples, then M = N × K;

[0102] The query set Q consists of randomly selected samples from the training set or continuous samples from the test set, and L represents the number of query set samples;

[0103] x i represents the support set sample, x j Represents a query set sample;

[0104] y i represents the support set sample label, y j Represents the query set sample label;

[0105] Step 442: Support Set Take the average of all feature vectors in and calculate the class prototype o for each category n ;

[0106]

[0107] Step 443: Create a prototype of each category n and f θ (x j ) Input the relational network model, and the relational network model outputs the relational score; the expression is:

[0108] rj,n=g ψ (Concat(on,f θ (xj))) (6)

[0109] Among them, Concat(·) represents the concatenation layer; it represents the class prototype o of each category. n and f θ (x j ) Input the splicing layer in the relational network model and the output of the splicing layer;

[0110] g ψ (·) represents the relational network model; ψ represents the parameters of the relational network model;

[0111] r j,n Represents the class prototype o n and query sample x j The relationship score between

[0112] Use the concatenation layer Concat(o n ,f θ (x j ))Cleverly connect the eigenvectors f θ (x i ) and f θ (x j ), thereby combining the data from the two collections.

[0113] The relational network model includes the concatenation layer, the flattening layer Faltten, the fully connected layer FC, the batch normalization BN, the linear rectification function ReLU, the fully connected layer FC, the batch normalization BN, the linear rectification function ReLU, the fully connected layer FC, the batch normalization BN, the linear rectification function ReLU, the fully connected layer FC, and the Sigmoid activation function.

[0114] The distance between the feature vector of the query sample and the class prototype is measured in the feature space. ψTo evaluate the distance between the query sample and the prototype. In order to develop a nonlinear and more adaptable distance metric between the query set Q and the support set S, a relational network RN that is more general and robust than a fixed metric is used. The architecture of the relational network RN for metric learning is as follows: Figure 3 shown.

[0115] Step 444: Train the relational network model until convergence to obtain a trained CNN network model; the specific process is as follows:

[0116] The input of the relational network model is the support set and query set of step 441, and the output of the relational network model is the relation score (which can quantify x i and x j The similarity between the scalar r between 0 and 1 j,n ), determine the category of the query sample based on the score;

[0117] The mean square error (MSE) loss function is used to optimize the relational network model. The loss function is as follows:

[0118]

[0119] The variable q represents the number of samples in the query set Q;

[0120] When the query set Q and the class prototype o n When matching, the binary variable The value is 1, and 0 if inconsistent;

[0121] The objective function of the relational network model is expressed as follows:

[0122]

[0123] Using CNN feature vectors as input, CNN feature embedding is implemented, and clustering is performed on the CNN feature vectors extracted through metric learning, which enhances the SEI performance of traditional CNN.

[0124] Metric learning network models such as Figure 3 As shown in the figure, it specifically includes 1 splicing layer, 1 Faltten layer, 4 fully connected layers and a Sigmoid layer.

[0125] The other steps and parameters are the same as those in the first to fourth embodiments.

[0126] The following examples are used to verify the beneficial effects of the present invention:

[0127] Example 1: Multiple signal processing methods, including HHT, CWD, ITD-Hilbert, GT, and CWT, were adopted to obtain the TF feature images of signals, and the influence of RFF representation of signals on SEI models was studied based on ResNet50 model and FS-SEI model. The results show that the FS-SEI model is always superior to the ResNet50 model under each RFF representation, highlighting the efficacy of the FS-SEI model.

[0128] Considering the influence of intelligent representation of RFF on SEI models, multiple signal processing methods, including HHT, CWD, ITD-Hilbert, GT, and CWT, were adopted to obtain the TF feature images of signals. Residual network (ResNet) is mainly used for its deep learning features, which effectively overcomes the vanishing gradient problem. This makes ResNet particularly suitable for our complex image recognition task, which can learn rich feature representations from data, thereby significantly improving model performance and generalization ability. Therefore, these TF feature images were individually input into ResNet and FS-SEI models for SEI, K = 500. As shown in Table 1, the FS-SEI model is always superior to the ResNet50 model under each RFF representation, highlighting the performance advantage of the FS-SEI model. Figure 4 As shown in Table 1, the FS-SEI model is always superior to the ResNet50 model under each RFF representation, highlighting the performance advantage of the FS-SEI model. Regarding the ResNet50 model, the performance difference between intelligent RFF representations is very obvious, and the CWD representation has a clear advantage. This is particularly evident in environments with low signal-to-noise ratio (SNR), where CWD features continue to exhibit superior recognition accuracy. On the other hand, while CWD, CWT, and Gabor performance is similar in the FS-SEI model when SNR is higher than 0 dB, CWD maintains the best performance. Notably, the FS-SEI model based on GT shows a significant performance decline at lower SNR, indicating lower robustness than other features.

[0129] Based on the experimental results presented in Table 2, the TF feature extraction techniques have been compared in terms of computational complexity and accuracy. The multiple feature vectors for machine learning through SVM and the features for DL models such as ResNet 50 were evaluated by generating the intelligent representation of the RFF of the signal. The computational complexity of CWD is 3731894 floating point operations per second (FLOPs) with an inference time of 0.80432 seconds, and the CWD features achieved an impressive accuracy of 95.6% at 0 dB with K = 500. This indicates that CWD maintains high accuracy while its computational demand and inference time remain within an acceptable range. The ITD-GSCM features, while exhibiting higher recognition performance with an accuracy of 88.1%, require significantly more computational resources than the other features used for SVM. Other features analyzed in the study, such as Bispec, HVG, and various EMD-based representations, showed varying degrees of performance with accuracy ranging from 59.5% to 79.9% at SNR = 0 dB. These features currently have lower computational cost, but do not reach the high accuracy level seen with CWD or ITD-GSCM. Therefore, the FS-SEI model proposed in this study employs CWD time-frequency maps as input, denoted as CWD-Metric.

[0130] Example 2: Analyzing the SEI results of the CWD-Metric model using CNN feature vectors of different dimensions at K = 20 to verify the reasonableness of setting the feature vector dimension to 1024;

[0131] The experimental results are shown in Figure 5 Figure 5 where a shows the SEI results at various SNRs, where the notation “F_x” denotes the results with a feature vector dimension of x, and “None” denotes the results using the traditional feature vector extraction network. It is observed that the CWD-Metric model performs best with a feature vector dimension of 1024 (denoted as F1024), consistently exhibiting superior performance at all SNRs. Furthermore, the CWD-Metric model with different dimensions consistently outperforms the traditional CNN structure, highlighting the high robustness of the proposed model while maintaining high accuracy. Figure 5 ​The computational and time complexity metrics of different methods are compared intuitively in Table B. It is worth noting that all models maintain similar training speed, about 5.95 iterations per second (it / s), despite the different dimensions of the feature vectors, which indicates that the training efficiency remains unchanged in the variation of feature size. In-depth study of the computational demand shows that while FLOP remains relatively stable in different models, there is a clear correlation between parameter count and the size of the feature vector. Specifically, F_2048 model requires significantly more parameters (6668182) than F_128 model, which only needs 2380694 parameters. This indicates that a larger feature vector dimension greatly increases the complexity of the model, which can affect memory usage and the scalability of the model. However, the model equipped with F_1024 achieved the highest accuracy of 91.7%, and provided a commendable balance between computational efficiency and model performance. In addition, the accuracy improvement from the smallest to the largest feature vector size (from 89.3% to 91.7%, and then to 90.6%) indicates that the return on increasing the feature vector size beyond a certain point will decrease.

[0132] Example 3: Performance of FS-SEI model under few-shot condition

[0133] When the number of training samples K = 1, 5, 10, 20, 50 and 100, the recognition rate of the proposed FS-SEI model under different signal-to-noise ratios was investigated under the condition of randomly selecting different numbers of training samples. The results are shown in Figure 6 Table C. Among them, CWD-CNN represents a common CNN model with CWD time-frequency diagram as input, reflecting the structure of the CNN feature extractor. As Figure 6As shown, CWD-Metric exhibits superior accuracy compared to CWD-CNN at all values of K, especially in low SNR and fewer samples. For example, at K = 1 and SNR of -5dB, the accuracy of the CWD-Metric model is about 20% higher than CWD-CNN. As the number of transmissions increases to 0, the gap narrows, but it is still evident that the performance of the CWD-Metric model is about 15% higher than CWD-CNN at the same SNR level. This trend continues as the value of K increases; however, the performance gap decreases as the number of samples increases. At K = 100 and SNR = 25dB, both models converge to similar high levels of accuracy, but the CWD-Metric model still shows a slight advantage. The robustness of the CWD-Metric model is particularly evident in low SNR conditions and with fewer training samples, as its accuracy remains relatively stable compared to the sharp decline observed in the CWD-CNN model. For example, at -5dB SNR and K = 1, the CWD-Metric maintains an accuracy close to 65%, while the CWD-CNN drops by about 45%. These results demonstrate the ability of the FS-SEI model to maintain high recognition accuracy even under challenging conditions. This is preferred in practical applications where limited labeled data or low-quality signals are common.

[0134] DPD techniques correct the non-linear effects of the amplifier, thereby reducing individual variance and degrading the recognition performance of SEI. In Figure 6 The subplots in FIG. 10c compare the CWD-Metric model (K = 10, DPD) with the best-performing ITD-GSCM model (K = 500, DPD). The results show that the CWD-Metric achieves comparable, and at SNR of 10 and 15dB, superior performance to the best-performing ITD-GSCM model, despite significantly fewer training samples. This indicates the robust adaptability of the CWD-Metric model with significantly fewer training samples. Extending this analysis, Figure 6 The subplots in FIG. 10c compare the CWD-Metric model (K = 10, DPD) with the best-performing ITD-GSCM model (K = 500, DPD). The results show that the CWD-Metric achieves comparable, and at SNR of 10 and 15dB, superior performance to the best-performing ITD-GSCM model, despite significantly fewer training samples. This indicates the robust adaptability of the CWD-Metric model with significantly fewer training samples. Extending this analysis,

[0135] The confusion matrices at SNR of -5dB and 10dB clearly illustrate the performance variation of the FS-SEI model in distinguishing between different transmitters, especially at different SNRs. In Figure 7In particular, the confusion matrix at -5 dB SNR indicates an overall accuracy of 77.07%. This lower accuracy is mainly due to the significant confusion between transmitters E5 and E6, which can be attributed to similar aging periods and amplifier characteristics, which complicate the differentiation of different classes at lower signal quality levels. In contrast, the model achieves a very high accuracy of 99.5% for transmitter E3, despite having the same aging period as E1 and E2. This particular accuracy can emphasize the different impact of different chip series on the detection capability, which suggests that chip variations play a crucial role in the model's ability to accurately differentiate transmitters. As Figure 7 As shown in FIG. b, when the SNR is increased to 10 dB, the overall accuracy significantly increases to 97.21%. The improved accuracy at higher SNR confirms that the model skillfully handles the identification challenges posed by transmitters from the same series and batch, which were previously prone to misclassification at lower SNR levels, under more precise signals. Based on these findings, it is evident that transmitters from the same series and batch are prone to misclassification under low SNR conditions; however, as the SNR increases, our model maintains a high identification rate. Furthermore, our model demonstrates a strong ability to identify transmitters from different series, even under small sample sizes and challenging SNR conditions. Notably, the CWD-Metric shows lower confusion for transmitters with different aging states (e.g., E4, E5, and E7), indicating the complex ability to identify subtle differences between transmitters.

[0136] Table 1 Signal parameter configuration

[0137]

[0138] Table 2 Performance comparison of different RFF representations

[0139]

[0140] The present application can also have other various embodiments, and it should be understood that various changes and modifications can be made by those skilled in the art to which the present application pertains without departing from the spirit and essential characteristics of the application, and it should be understood that these changes and modifications are intended to be included within the scope of the claims appended hereto.

Claims

1. A method for identifying individual radiation sources in a finite sample scenario under digital predistortion, characterized by: The specific process of the method is: Step 1: Preprocess the collected signals to obtain HHT graph, ITD-Hilbert graph, CWT graph, CWD graph and GT graph; The HHT is Hilbert-Huang transform; The ITD-Hilbert is Hilbert transform; The CWT is continuous wavelet transform; The CWD is Choi-Williams distribution; The GT is Gabor transform; Step 2: Preprocess the HHT graph, ITD-Hilbert graph, CWT graph, CWD graph and GT graph respectively to construct the dataset; Step 3: Build the FS-SEI network model; The FS-SEI network model includes the CNN network model and the relational network model; The CNN network model includes a feature extractor and a classifier in sequence; The specific process is: Step 3: Build a CNN network model. The CNN network model includes a feature extractor and a classifier in sequence. The feature extractor includes a first convolution block, a maximum pooling layer, a second convolution block, a maximum pooling layer, a third convolution block, a maximum pooling layer, a flattening layer Faltten, a fully connected layer FC, a batch normalization BN, and a linear rectification function ReLU in sequence; The classifier includes a fully connected layer FC, a batch normalization BN, a linear rectification function ReLU, a fully connected layer FC, a batch normalization BN, a linear rectification function ReLU, and a Softmax layer in sequence; Each of the first convolution block, the second convolution block, and the third convolution block includes a convolution layer, a batch normalization BN, and a linear rectification function ReLU in sequence; Step 32: Build a relationship network model; The relational network model includes the concatenation layer, the flattening layer Faltten, the fully connected layer FC, the batch normalization BN, the linear rectification function ReLU, the fully connected layer FC, the batch normalization BN, the linear rectification function ReLU, the fully connected layer FC, the batch normalization BN, the linear rectification function ReLU, the fully connected layer FC, and the Sigmoid activation function. Step 4: Train the FS-SEI network model to obtain a trained FS-SEI network model; Step 5: Input the test set into the trained FS-SEI network model, and the trained FS-SEI network model outputs the category of the test set.

2. The method for identifying individual radiation sources in a finite sample scenario under digital predistortion according to claim 1, characterized in that: In the step 1, the collected signal is preprocessed to obtain the HHT map, ITD-Hilbert map, CWT map, CWD map and GT map; the specific process is: Step 1. Collect signal samples from different types of transmitters; Perform wavelet denoising on the collected signal samples to obtain denoised signal samples; Pulse extraction is performed on the denoised signal samples, with every 10 pulses as one signal sample, and 500 signal samples are obtained; The 10 pulses in each signal sample are extracted separately to obtain a signal sample containing only a single pulse; A total of 5000 signal samples containing only single pulses were obtained; Step 12: Perform Hilbert-Huang transform on the signal containing only a single pulse obtained in step 11 to obtain an HHT time-frequency diagram; Step 13: first perform intrinsic time scale decomposition on the signal containing only a single pulse obtained in step 11 to obtain a rotation component, then calculate the Hilbert spectrum of the rotation component to obtain an ITD-Hilbert time-frequency diagram; Step 14: Use Morlet wavelet as mother wavelet ψ(·), scale and translate the mother wavelet ψ(·) in sequence to generate A wavelet functions; The convolution of the signal x(t) containing only a single pulse obtained in step 1 with each wavelet function ψ(t) yields the CWT time-frequency diagram; the expression is: Among them, a represents the scale parameter of the wavelet function, b represents the translation parameter, ψ * (·) represents the complex conjugate of the mother wavelet, and t represents time; Step 15: Calculate the Choi-Williams distribution of the pulse signal and obtain the CWD time-frequency diagram; the expression is: Where x(t) represents the signal containing only a single pulse obtained in step 1, and x * (t) represents the complex conjugate of x(t), σ represents the parameter; f represents the frequency; t represents the time; τ represents the time delay variable; j represents the imaginary unit, j 2 =-1; Step 16: Perform Gabor transform on the signal containing only a single pulse obtained in step 11 to obtain a GT time-frequency map; Step 17: Store the HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram, and GT time-frequency diagram in a size of 700×525.

3. The method for identifying individual radiation sources in a finite sample scenario under digital predistortion according to claim 2, characterized in that: In the step 2, the HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram and GT time-frequency diagram are preprocessed to construct a data set; the specific process is: Step 21: The signal sample data set containing only a single pulse obtained in step 11 is randomly divided into a training set and a test set in a ratio of 7:3; Step 22: Normalize the HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram, and GT time-frequency diagram obtained in step 1 to obtain the normalized HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram, and GT time-frequency diagram, and crop the normalized HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram, and GT time-frequency diagram into HHT time-frequency diagrams, ITD-Hilbert time-frequency diagrams, CWT time-frequency diagrams, CWD time-frequency diagrams, and GT time-frequency diagrams of a size of 100×100, respectively. Step 2 and 3: Put the cropped HHT time-frequency diagram, ITD-Hilbert time-frequency diagram, CWT time-frequency diagram, CWD time-frequency diagram, and GT time-frequency diagram corresponding to the same type of transmitter into the same folder. Each folder contains five subfolders, and each subfolder corresponds to a type of time-frequency diagram; A folder represents the secondary representation of the signal in different forms of time-frequency diagrams corresponding to the same type of transmitter.

4. The method for identifying individual radiation sources in a finite sample scenario under digital predistortion according to claim 3, characterized in that: In step 4, the FS-SEI network model is trained to obtain a trained FS-SEI network model. The specific process is as follows: Step 4.1: Input the secondary representation of the signal into the CNN network model, and the CNN network model outputs the emitter type result; the specific process is: The cropped HHT time-frequency graph, ITD-Hilbert time-frequency graph, CWT time-frequency graph, CWD time-frequency graph, and GT time-frequency graph corresponding to the secondary representation of the signal are input into the feature extractor, and the feature extractor outputs a 1024-dimensional feature vector; The 1024-dimensional feature vector is input into the classifier, and the classifier outputs the emitter type result; Step 42: Input the 1024-dimensional feature vector into the relational network model, and the relational network model outputs the relation score; Step 43: Train the CNN network model until convergence to obtain a trained CNN network model; the specific process is as follows: Among them, J(θ) is the loss function; Represents the secondary representation of the signal, output represents the probability that the signal belongs to each emitter category; C, H, W, and N represent the number of channels, height, width, and category, respectively. represents the set of real numbers; M represents the total number of training samples; i and n represent the indexes of training samples and emitter categories, respectively; θ represents the parameters of the CNN network model; When the true label of the i-th training sample is consistent with n, the p value is 1; otherwise, the p value is 0; P θ Represents the output of the softmax layer in the classifier; Step 4: Train the relational network model until convergence to obtain a trained CNN network model. The specific process is as follows: Step 441: Define the support set and queryset Among them, f θ (x i ) represents the feature extractor f θ The CNN feature vector extracted from the examples in the support set S, f θ (x j ) represents the CNN feature vector extracted by the feature extractor from the examples of the query set Q; Where M represents the number of support set samples, S includes all training set samples, and when the support set S contains N emitter categories and each category has K samples, then M = N × K; The query set Q consists of randomly selected samples from the training set or continuous samples from the test set, and L represents the number of query set samples; x i represents the support set sample, x j Represents a query set sample; y i represents the support set sample label, y j Represents the query set sample label; Step 442: Support Set Take the average of all feature vectors in and calculate the class prototype o for each category n ; Step 443: Create a prototype of each category n and f θ (x j ) Input the relational network model, and the relational network model outputs the relational score; the expression is: r j,n =g ψ (Concat(o n ,f θ (x j ))) (6) Among them, Concat(·) represents the concatenation layer; g ψ (·) represents the relational network model; ψ represents the parameters of the relational network model; r j,n Represents the class prototype o n and query sample x j The relationship score between Step 444: Train the relational network model until convergence to obtain a trained CNN network model; the specific process is as follows: The input of the relational network model is the support set and query set of step 441. The output of the relational network model is the relation score, and the category of the query sample is determined based on the score. The mean square error loss function is used to optimize the relational network model. The loss function is as follows: The variable q represents the number of samples in the query set Q; When the query set Q and the class prototype o n When matching, the binary variable The value is 1, and 0 if inconsistent; The objective function of the relational network model is expressed as follows:

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